IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v312y2022i1d10.1007_s10479-019-03429-2.html
   My bibliography  Save this article

Reliability prediction based on Birnbaum–Saunders model and its application to smart meter

Author

Listed:
  • Dan Xu

    (Beihang University)

  • Jiaolan He

    (Beihang University)

  • Zhou Yang

    (Guangxi Power Grid Co, Ltd
    Tsinghua University)

Abstract

For accelerated degradation testing, data analysis based on stochastic process has been drawn much attention. However, there is significant difference in reliability prediction based on different process. This paper proposes a unified distribution model combined with a stochastic process model in multiple accelerated stress degradation test. To solve the problem of heterogeneous population of pseudo failure data, the Birnbaum–Saunders model is considered as a unified distribution model for different Gaussian family process. To give an example, a detailed proof for substituting the Birnbaum–Saunders model for the first-passage time of Wiener process is provided. Then, the influence of the parameters of the Birnbaum–Saunders model was analyzed, which provided a basis for the Birnbaum–Saunders model to be selected as a unified model. To verify presented model, a case study of Smart Meter ADT is conducted. And the obtained results of this work is compared with former work of Smart Meter ADT modeling, which verifies the effectiveness of the proposed modeling method to heterogeneous population.

Suggested Citation

  • Dan Xu & Jiaolan He & Zhou Yang, 2022. "Reliability prediction based on Birnbaum–Saunders model and its application to smart meter," Annals of Operations Research, Springer, vol. 312(1), pages 519-532, May.
    • Handle: RePEc:spr:annopr:v:312:y:2022:i:1:d:10.1007_s10479-019-03429-2
    DOI: 10.1007/s10479-019-03429-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-019-03429-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10479-019-03429-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wang, Xiaolin & Balakrishnan, Narayanaswamy & Guo, Bo, 2014. "Residual life estimation based on a generalized Wiener degradation process," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 13-23.
    2. Haitao Liao & Zhigang Tian, 2013. "A framework for predicting the remaining useful life of a single unit under time-varying operating conditions," IISE Transactions, Taylor & Francis Journals, vol. 45(9), pages 964-980.
    3. Le Liu & Xiao-Yang Li & Enrico Zio & Rui Kang & Tong-Min Jiang, 2017. "Model Uncertainty in Accelerated Degradation Testing Analysis," Post-Print hal-01652218, HAL.
    4. Lemonte, Artur J. & Cribari-Neto, Francisco & Vasconcellos, Klaus L.P., 2007. "Improved statistical inference for the two-parameter Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4656-4681, May.
    5. Kundu, Debasis & Kannan, Nandini & Balakrishnan, N., 2008. "On the hazard function of Birnbaum-Saunders distribution and associated inference," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2692-2702, January.
    6. Zhi‐Sheng Ye & Min Xie, 2015. "Stochastic modelling and analysis of degradation for highly reliable products," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 31(1), pages 16-32, January.
    7. Gómez, Héctor W. & Olivares-Pacheco, Juan F. & Bolfarine, Heleno, 2009. "An extension of the generalized Birnbaum-Saunders distribution," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 331-338, February.
    8. Lemonte, Artur J. & Cordeiro, Gauss M., 2009. "Birnbaum-Saunders nonlinear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4441-4452, October.
    9. Wang, Lizhi & Pan, Rong & Li, Xiaoyang & Jiang, Tongmin, 2013. "A Bayesian reliability evaluation method with integrated accelerated degradation testing and field information," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 38-47.
    10. Anders Holst, 2015. "Optimal test planning for High Cycle Fatigue limit testing," Annals of Operations Research, Springer, vol. 224(1), pages 101-110, January.
    11. Lin, Kunsong & Chen, Yunxia & Xu, Dan, 2017. "Reliability assessment model considering heterogeneous population in a multiple stresses accelerated test," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 134-143.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Le Liu & Xiao-Yang Li & Enrico Zio & Rui Kang & Tong-Min Jiang, 2017. "Model Uncertainty in Accelerated Degradation Testing Analysis," Post-Print hal-01652218, HAL.
    2. Bhatti, Chad R., 2010. "The Birnbaum–Saunders autoregressive conditional duration model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2062-2078.
    3. Ortega, Edwin M.M. & Cordeiro, Gauss M. & Lemonte, Artur J., 2012. "A log-linear regression model for the β-Birnbaum–Saunders distribution with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 698-718.
    4. Peihua Jiang, 2022. "Statistical Inference of Wiener Constant-Stress Accelerated Degradation Model with Random Effects," Mathematics, MDPI, vol. 10(16), pages 1-18, August.
    5. Zhang, Zhengxin & Si, Xiaosheng & Hu, Changhua & Lei, Yaguo, 2018. "Degradation data analysis and remaining useful life estimation: A review on Wiener-process-based methods," European Journal of Operational Research, Elsevier, vol. 271(3), pages 775-796.
    6. Li, Ai-Ping & Xie, Feng-Chang, 2012. "Diagnostics for a class of survival regression models with heavy-tailed errors," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4204-4214.
    7. Liu, Di & Wang, Shaoping & Zhang, Chao & Tomovic, Mileta, 2018. "Bayesian model averaging based reliability analysis method for monotonic degradation dataset based on inverse Gaussian process and Gamma process," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 25-38.
    8. Lemonte, Artur J. & Cordeiro, Gauss M., 2010. "Asymptotic skewness in Birnbaum-Saunders nonlinear regression models," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 892-898, May.
    9. Lemonte, Artur J., 2013. "A new extended Birnbaum–Saunders regression model for lifetime modeling," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 34-50.
    10. Artur J. Lemonte & Alexandre G. Patriota, 2011. "Influence diagnostics in Birnbaum--Saunders nonlinear regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(5), pages 871-884, February.
    11. Liu, Di & Wang, Shaoping & Cui, Xiaoyu, 2022. "An artificial neural network supported Wiener process based reliability estimation method considering individual difference and measurement error," Reliability Engineering and System Safety, Elsevier, vol. 218(PB).
    12. Zhou, Shirong & Tang, Yincai & Xu, Ancha, 2021. "A generalized Wiener process with dependent degradation rate and volatility and time-varying mean-to-variance ratio," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    13. Huang, Jianlin & Golubović, Dušan S & Koh, Sau & Yang, Daoguo & Li, Xiupeng & Fan, Xuejun & Zhang, G.Q., 2016. "Lumen degradation modeling of white-light LEDs in step stress accelerated degradation test," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 152-159.
    14. Wang, Xiaofei & Wang, Bing Xing & Jiang, Pei Hua & Hong, Yili, 2020. "Accurate reliability inference based on Wiener process with random effects for degradation data," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    15. Chen, Wen-Bin & Li, Xiao-Yang & Kang, Rui, 2022. "Integration for degradation analysis with multi-source ADT datasets considering dataset discrepancies and epistemic uncertainties," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    16. Zhao, Xiujie & Chen, Piao & Gaudoin, Olivier & Doyen, Laurent, 2021. "Accelerated degradation tests with inspection effects," European Journal of Operational Research, Elsevier, vol. 292(3), pages 1099-1114.
    17. Filidor Vilca & Camila Borelli Zeller & Gauss M. Cordeiro, 2015. "The sinh-normal/independent nonlinear regression model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(8), pages 1659-1676, August.
    18. Kim, Seong-Joon & Mun, Byeong Min & Bae, Suk Joo, 2019. "A cost-driven reliability demonstration plan based on accelerated degradation tests," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 226-239.
    19. Cordeiro, Gauss M. & Lemonte, Artur J., 2011. "The [beta]-Birnbaum-Saunders distribution: An improved distribution for fatigue life modeling," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1445-1461, March.
    20. Zhang, Ao & Wang, Zhihua & Bao, Rui & Liu, Chengrui & Wu, Qiong & Cao, Shihao, 2023. "A novel failure time estimation method for degradation analysis based on general nonlinear Wiener processes," Reliability Engineering and System Safety, Elsevier, vol. 230(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:312:y:2022:i:1:d:10.1007_s10479-019-03429-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.